Mathematics Question from JEE Main 2026 · 28 January, Shift 1

Let $PQR$ be a triangle such that $\vec{PQ}=-2\hat i-\hat j+2\hat k,\quad \vec{PR}=a\hat i+b\hat j-4\hat k,\ a,b\in\mathbb{Z}.$ Let $S$ be the point on $QR$ which is equidistant from the lines $PQ$ and $PR$. If $|\vec{PR}|=9$ and $\vec{PS}=\hat i-7\hat j+2\hat k,$ then the value of $3a-4b$ is: